#ifndef __Matrix4__
#define __Matrix4__

// Precompiler options
#include "Prerequisites.h"

#include "Vec3f.h"
#include "Matrix3.h"
#include "Vec4f.h"
#include "Quaternion.h"

/** \addtogroup Core
 *  @{
 */
/** \addtogroup Math
 *  @{
 */
/** Class encapsulating a standard 4x4 homogeneous matrix.
  @remarks
  OGRE uses column vectors when applying matrix multiplications,
  This means a vector is represented as a single column, 4-row
  matrix. This has the effect that the transformations implemented
  by the matrices happens right-to-left e.g. if vector V is to be
  transformed by M1 then M2 then M3, the calculation would be
  M3 * M2 * M1 * V. The order that matrices are concatenated is
  vital since matrix multiplication is not commutative, i.e. you
  can get a different result if you concatenate in the wrong order.
  @par
  The use of column vectors and right-to-left ordering is the
  standard in most mathematical texts, and is the same as used in
  OpenGL. It is, however, the opposite of Direct3D, which has
  inexplicably chosen to differ from the accepted standard and uses
  row vectors and left-to-right matrix multiplication.
  @par
  OGRE deals with the differences between D3D and OpenGL etc.
  internally when operating through different render systems. OGRE
  users only need to conform to standard maths conventions, i.e.
  right-to-left matrix multiplication, (OGRE transposes matrices it
  passes to D3D to compensate).
  @par
  The generic form M * V which shows the layout of the matrix 
  entries is shown below:
  <pre>
  [ m[0][0]  m[0][1]  m[0][2]  m[0][3] ]   {x}
  | m[1][0]  m[1][1]  m[1][2]  m[1][3] | * {y}
  | m[2][0]  m[2][1]  m[2][2]  m[2][3] |   {z}
  [ m[3][0]  m[3][1]  m[3][2]  m[3][3] ]   {1}
  </pre>
  */
class Matrix4
{
	protected:
		/// The matrix entries, indexed by [row][col].
		union {
			float m[4][4];
			float _m[16];
		};
	public:
		/** Default constructor.
		  @note
		  It does <b>NOT</b> initialize the matrix for efficiency.
		  */
		inline Matrix4()
		{
		}

		inline Matrix4(
				float m00, float m01, float m02, float m03,
				float m10, float m11, float m12, float m13,
				float m20, float m21, float m22, float m23,
				float m30, float m31, float m32, float m33 )
		{
			m[0][0] = m00;
			m[0][1] = m01;
			m[0][2] = m02;
			m[0][3] = m03;
			m[1][0] = m10;
			m[1][1] = m11;
			m[1][2] = m12;
			m[1][3] = m13;
			m[2][0] = m20;
			m[2][1] = m21;
			m[2][2] = m22;
			m[2][3] = m23;
			m[3][0] = m30;
			m[3][1] = m31;
			m[3][2] = m32;
			m[3][3] = m33;
		}

		/** Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling 3x3 matrix.
		*/

		inline Matrix4(const Matrix3& m3x3)
		{
			operator=(IDENTITY);
			operator=(m3x3);
		}

		/** Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion.
		*/

		inline Matrix4(const Quaternion& rot)
		{
			Matrix3 m3x3;
			rot.ToRotationMatrix(m3x3);
			operator=(IDENTITY);
			operator=(m3x3);
		}


		/** Exchange the contents of this matrix with another. 
		*/
		inline void swap(Matrix4& other)
		{
			std::swap(m[0][0], other.m[0][0]);
			std::swap(m[0][1], other.m[0][1]);
			std::swap(m[0][2], other.m[0][2]);
			std::swap(m[0][3], other.m[0][3]);
			std::swap(m[1][0], other.m[1][0]);
			std::swap(m[1][1], other.m[1][1]);
			std::swap(m[1][2], other.m[1][2]);
			std::swap(m[1][3], other.m[1][3]);
			std::swap(m[2][0], other.m[2][0]);
			std::swap(m[2][1], other.m[2][1]);
			std::swap(m[2][2], other.m[2][2]);
			std::swap(m[2][3], other.m[2][3]);
			std::swap(m[3][0], other.m[3][0]);
			std::swap(m[3][1], other.m[3][1]);
			std::swap(m[3][2], other.m[3][2]);
			std::swap(m[3][3], other.m[3][3]);
		}

		inline float* operator [] ( size_t iRow )
		{
			assert( iRow < 4 );
			return m[iRow];
		}

		inline const float *operator [] ( size_t iRow ) const
		{
			assert( iRow < 4 );
			return m[iRow];
		}

		inline Matrix4 concatenate(const Matrix4 &m2) const
		{
			Matrix4 r;
			r.m[0][0] = m[0][0] * m2.m[0][0] + m[0][1] * m2.m[1][0] + m[0][2] * m2.m[2][0] + m[0][3] * m2.m[3][0];
			r.m[0][1] = m[0][0] * m2.m[0][1] + m[0][1] * m2.m[1][1] + m[0][2] * m2.m[2][1] + m[0][3] * m2.m[3][1];
			r.m[0][2] = m[0][0] * m2.m[0][2] + m[0][1] * m2.m[1][2] + m[0][2] * m2.m[2][2] + m[0][3] * m2.m[3][2];
			r.m[0][3] = m[0][0] * m2.m[0][3] + m[0][1] * m2.m[1][3] + m[0][2] * m2.m[2][3] + m[0][3] * m2.m[3][3];

			r.m[1][0] = m[1][0] * m2.m[0][0] + m[1][1] * m2.m[1][0] + m[1][2] * m2.m[2][0] + m[1][3] * m2.m[3][0];
			r.m[1][1] = m[1][0] * m2.m[0][1] + m[1][1] * m2.m[1][1] + m[1][2] * m2.m[2][1] + m[1][3] * m2.m[3][1];
			r.m[1][2] = m[1][0] * m2.m[0][2] + m[1][1] * m2.m[1][2] + m[1][2] * m2.m[2][2] + m[1][3] * m2.m[3][2];
			r.m[1][3] = m[1][0] * m2.m[0][3] + m[1][1] * m2.m[1][3] + m[1][2] * m2.m[2][3] + m[1][3] * m2.m[3][3];

			r.m[2][0] = m[2][0] * m2.m[0][0] + m[2][1] * m2.m[1][0] + m[2][2] * m2.m[2][0] + m[2][3] * m2.m[3][0];
			r.m[2][1] = m[2][0] * m2.m[0][1] + m[2][1] * m2.m[1][1] + m[2][2] * m2.m[2][1] + m[2][3] * m2.m[3][1];
			r.m[2][2] = m[2][0] * m2.m[0][2] + m[2][1] * m2.m[1][2] + m[2][2] * m2.m[2][2] + m[2][3] * m2.m[3][2];
			r.m[2][3] = m[2][0] * m2.m[0][3] + m[2][1] * m2.m[1][3] + m[2][2] * m2.m[2][3] + m[2][3] * m2.m[3][3];

			r.m[3][0] = m[3][0] * m2.m[0][0] + m[3][1] * m2.m[1][0] + m[3][2] * m2.m[2][0] + m[3][3] * m2.m[3][0];
			r.m[3][1] = m[3][0] * m2.m[0][1] + m[3][1] * m2.m[1][1] + m[3][2] * m2.m[2][1] + m[3][3] * m2.m[3][1];
			r.m[3][2] = m[3][0] * m2.m[0][2] + m[3][1] * m2.m[1][2] + m[3][2] * m2.m[2][2] + m[3][3] * m2.m[3][2];
			r.m[3][3] = m[3][0] * m2.m[0][3] + m[3][1] * m2.m[1][3] + m[3][2] * m2.m[2][3] + m[3][3] * m2.m[3][3];

			return r;
		}

		/** Matrix concatenation using '*'.
		*/
		inline Matrix4 operator * ( const Matrix4 &m2 ) const
		{
			return concatenate( m2 );
		}

		/** Vector transformation using '*'.
		  @remarks
		  Transforms the given 3-D vector by the matrix, projecting the 
		  result back into <i>w</i> = 1.
		  @note
		  This means that the initial <i>w</i> is considered to be 1.0,
		  and then all the tree elements of the resulting 3-D vector are
		  divided by the resulting <i>w</i>.
		  */
		inline Vector3f operator * ( const Vector3f &v ) const
		{
			Vector3f r;

			float fInvW = 1.0f / ( m[3][0] * v.x + m[3][1] * v.y + m[3][2] * v.z + m[3][3] );

			r.x = ( m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] ) * fInvW;
			r.y = ( m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] ) * fInvW;
			r.z = ( m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] ) * fInvW;

			return r;
		}
		inline Vector4f operator * (const Vector4f& v) const
		{
			return Vector4f(
					m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] * v.w, 
					m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] * v.w,
					m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] * v.w,
					m[3][0] * v.x + m[3][1] * v.y + m[3][2] * v.z + m[3][3] * v.w
					);
		}

		/** Matrix addition.
		*/
		inline Matrix4 operator + ( const Matrix4 &m2 ) const
		{
			Matrix4 r;

			r.m[0][0] = m[0][0] + m2.m[0][0];
			r.m[0][1] = m[0][1] + m2.m[0][1];
			r.m[0][2] = m[0][2] + m2.m[0][2];
			r.m[0][3] = m[0][3] + m2.m[0][3];

			r.m[1][0] = m[1][0] + m2.m[1][0];
			r.m[1][1] = m[1][1] + m2.m[1][1];
			r.m[1][2] = m[1][2] + m2.m[1][2];
			r.m[1][3] = m[1][3] + m2.m[1][3];

			r.m[2][0] = m[2][0] + m2.m[2][0];
			r.m[2][1] = m[2][1] + m2.m[2][1];
			r.m[2][2] = m[2][2] + m2.m[2][2];
			r.m[2][3] = m[2][3] + m2.m[2][3];

			r.m[3][0] = m[3][0] + m2.m[3][0];
			r.m[3][1] = m[3][1] + m2.m[3][1];
			r.m[3][2] = m[3][2] + m2.m[3][2];
			r.m[3][3] = m[3][3] + m2.m[3][3];

			return r;
		}

		/** Matrix subtraction.
		*/
		inline Matrix4 operator - ( const Matrix4 &m2 ) const
		{
			Matrix4 r;
			r.m[0][0] = m[0][0] - m2.m[0][0];
			r.m[0][1] = m[0][1] - m2.m[0][1];
			r.m[0][2] = m[0][2] - m2.m[0][2];
			r.m[0][3] = m[0][3] - m2.m[0][3];

			r.m[1][0] = m[1][0] - m2.m[1][0];
			r.m[1][1] = m[1][1] - m2.m[1][1];
			r.m[1][2] = m[1][2] - m2.m[1][2];
			r.m[1][3] = m[1][3] - m2.m[1][3];

			r.m[2][0] = m[2][0] - m2.m[2][0];
			r.m[2][1] = m[2][1] - m2.m[2][1];
			r.m[2][2] = m[2][2] - m2.m[2][2];
			r.m[2][3] = m[2][3] - m2.m[2][3];

			r.m[3][0] = m[3][0] - m2.m[3][0];
			r.m[3][1] = m[3][1] - m2.m[3][1];
			r.m[3][2] = m[3][2] - m2.m[3][2];
			r.m[3][3] = m[3][3] - m2.m[3][3];

			return r;
		}

		/** Tests 2 matrices for equality.
		*/
		inline bool operator == ( const Matrix4& m2 ) const
		{
			if( 
					m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||
					m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||
					m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] ||
					m[3][0] != m2.m[3][0] || m[3][1] != m2.m[3][1] || m[3][2] != m2.m[3][2] || m[3][3] != m2.m[3][3] )
				return false;
			return true;
		}

		/** Tests 2 matrices for inequality.
		*/
		inline bool operator != ( const Matrix4& m2 ) const
		{
			if( 
					m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||
					m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||
					m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] ||
					m[3][0] != m2.m[3][0] || m[3][1] != m2.m[3][1] || m[3][2] != m2.m[3][2] || m[3][3] != m2.m[3][3] )
				return true;
			return false;
		}

		/** Assignment from 3x3 matrix.
		*/
		inline void operator = ( const Matrix3& mat3 )
		{
			m[0][0] = mat3.m[0][0]; m[0][1] = mat3.m[0][1]; m[0][2] = mat3.m[0][2];
			m[1][0] = mat3.m[1][0]; m[1][1] = mat3.m[1][1]; m[1][2] = mat3.m[1][2];
			m[2][0] = mat3.m[2][0]; m[2][1] = mat3.m[2][1]; m[2][2] = mat3.m[2][2];
		}

		//转置矩阵
		inline Matrix4 transpose(void) const
		{
			return Matrix4(m[0][0], m[1][0], m[2][0], m[3][0],
					m[0][1], m[1][1], m[2][1], m[3][1],
					m[0][2], m[1][2], m[2][2], m[3][2],
					m[0][3], m[1][3], m[2][3], m[3][3]);
		}

		/*
		   -----------------------------------------------------------------------
		   Translation Transformation
		   -----------------------------------------------------------------------
		   */
		/** Sets the translation transformation part of the matrix.
		*/
		inline void setTrans( const Vector3f& v )
		{
			m[0][3] = v.x;
			m[1][3] = v.y;
			m[2][3] = v.z;
		}

		/** Extracts the translation transformation part of the matrix.
		*/
		inline Vector3f getTrans() const
		{
			return Vector3f(m[0][3], m[1][3], m[2][3]);
		}


		/** Builds a translation matrix
		*/
		inline void makeTrans( const Vector3f& v )
		{
			m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = v.x;
			m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = v.y;
			m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = v.z;
			m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0;
		}

		inline void makeTrans( float tx, float ty, float tz )
		{
			m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = tx;
			m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = ty;
			m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = tz;
			m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0;
		}

		/** Gets a translation matrix.
		*/
		inline static Matrix4 getTrans( const Vector3f& v )
		{
			Matrix4 r;

			r.m[0][0] = 1.0; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = v.x;
			r.m[1][0] = 0.0; r.m[1][1] = 1.0; r.m[1][2] = 0.0; r.m[1][3] = v.y;
			r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = 1.0; r.m[2][3] = v.z;
			r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;

			return r;
		}

		/** Gets a translation matrix - variation for not using a vector.
		*/
		inline static Matrix4 getTrans( float t_x, float t_y, float t_z )
		{
			Matrix4 r;

			r.m[0][0] = 1.0; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = t_x;
			r.m[1][0] = 0.0; r.m[1][1] = 1.0; r.m[1][2] = 0.0; r.m[1][3] = t_y;
			r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = 1.0; r.m[2][3] = t_z;
			r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;

			return r;
		}

		/*
		   -----------------------------------------------------------------------
		   Scale Transformation
		   -----------------------------------------------------------------------
		   */
		/** Sets the scale part of the matrix.
		*/
		inline void setScale( const Vector3f& v )
		{
			m[0][0] = v.x;
			m[1][1] = v.y;
			m[2][2] = v.z;
		}

		/** Gets a scale matrix.
		*/
		inline static Matrix4 getScale( const Vector3f& v )
		{
			Matrix4 r;
			r.m[0][0] = v.x; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = 0.0;
			r.m[1][0] = 0.0; r.m[1][1] = v.y; r.m[1][2] = 0.0; r.m[1][3] = 0.0;
			r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = v.z; r.m[2][3] = 0.0;
			r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;

			return r;
		}

		/** Gets a scale matrix - variation for not using a vector.
		*/
		inline static Matrix4 getScale( float s_x, float s_y, float s_z )
		{
			Matrix4 r;
			r.m[0][0] = s_x; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = 0.0;
			r.m[1][0] = 0.0; r.m[1][1] = s_y; r.m[1][2] = 0.0; r.m[1][3] = 0.0;
			r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = s_z; r.m[2][3] = 0.0;
			r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;

			return r;
		}

		/** Extracts the rotation / scaling part of the Matrix as a 3x3 matrix. 
		  @param m3x3 Destination Matrix3
		  */
		inline void extract3x3Matrix(Matrix3& m3x3) const
		{
			m3x3.m[0][0] = m[0][0];
			m3x3.m[0][1] = m[0][1];
			m3x3.m[0][2] = m[0][2];
			m3x3.m[1][0] = m[1][0];
			m3x3.m[1][1] = m[1][1];
			m3x3.m[1][2] = m[1][2];
			m3x3.m[2][0] = m[2][0];
			m3x3.m[2][1] = m[2][1];
			m3x3.m[2][2] = m[2][2];

		}

		/** Determines if this matrix involves a scaling. */
		inline bool hasScale() const
		{
			// check magnitude of column vectors (==local axes)
			float t = m[0][0] * m[0][0] + m[1][0] * m[1][0] + m[2][0] * m[2][0];
			if (!Math::floatEqual(t, 1.0, (float)1e-04))
				return true;
			t = m[0][1] * m[0][1] + m[1][1] * m[1][1] + m[2][1] * m[2][1];
			if (!Math::floatEqual(t, 1.0, (float)1e-04))
				return true;
			t = m[0][2] * m[0][2] + m[1][2] * m[1][2] + m[2][2] * m[2][2];
			if (!Math::floatEqual(t, 1.0, (float)1e-04))
				return true;

			return false;
		}

		/** Determines if this matrix involves a negative scaling. */
		inline bool hasNegativeScale() const
		{
			return determinant() < 0;
		}

		/** Extracts the rotation / scaling part as a quaternion from the Matrix.
		*/
		inline Quaternion extractQuaternion() const
		{
			Matrix3 m3x3;
			extract3x3Matrix(m3x3);
			return Quaternion(m3x3);
		}

		static const Matrix4 ZERO;
		static const Matrix4 IDENTITY;
		/** Useful little matrix which takes 2D clipspace {-1, 1} to {0,1}
		  and inverts the Y. */
		static const Matrix4 CLIPSPACE2DTOIMAGESPACE;

		inline Matrix4 operator*(float scalar) const
		{
			return Matrix4(
					scalar*m[0][0], scalar*m[0][1], scalar*m[0][2], scalar*m[0][3],
					scalar*m[1][0], scalar*m[1][1], scalar*m[1][2], scalar*m[1][3],
					scalar*m[2][0], scalar*m[2][1], scalar*m[2][2], scalar*m[2][3],
					scalar*m[3][0], scalar*m[3][1], scalar*m[3][2], scalar*m[3][3]);
		}

		/** Function for writing to a stream.
		*/
		inline friend std::ostream& operator <<
			( std::ostream& o, const Matrix4& mat )
			{
				o << "Matrix4(";
				for (size_t i = 0; i < 4; ++i)
				{
					o << " row" << (unsigned)i << "{";
					for(size_t j = 0; j < 4; ++j)
					{
						o << mat[i][j] << " ";
					}
					o << "}";
				}
				o << ")";
				return o;
			}

		Matrix4 adjoint() const;
		float determinant() const;
		Matrix4 inverse() const;

		/** Building a Matrix4 from orientation / scale / position.
		  @remarks
		  Transform is performed in the order scale, rotate, translation, i.e. translation is independent
		  of orientation axes, scale does not affect size of translation, rotation and scaling are always
		  centered on the origin.
		  */
		void makeTransform(const Vector3f& position, const Vector3f& scale, const Quaternion& orientation);

		/** Building an inverse Matrix4 from orientation / scale / position.
		  @remarks
		  As makeTransform except it build the inverse given the same data as makeTransform, so
		  performing -translation, -rotate, 1/scale in that order.
		  */
		void makeInverseTransform(const Vector3f& position, const Vector3f& scale, const Quaternion& orientation);

		/** Decompose a Matrix4 to orientation / scale / position.
		*/
		void decomposition(Vector3f& position, Vector3f& scale, Quaternion& orientation) const;

		/** Check whether or not the matrix is affine matrix.
		  @remarks
		  An affine matrix is a 4x4 matrix with row 3 equal to (0, 0, 0, 1),
		  e.g. no projective coefficients.
		  */
		inline bool isAffine(void) const
		{
			return m[3][0] == 0 && m[3][1] == 0 && m[3][2] == 0 && m[3][3] == 1;
		}

		/** Returns the inverse of the affine matrix.
		  @note
		  The matrix must be an affine matrix. @see Matrix4::isAffine.
		  */
		Matrix4 inverseAffine(void) const;

		/** Concatenate two affine matrices.
		  @note
		  The matrices must be affine matrix. @see Matrix4::isAffine.
		  */
		inline Matrix4 concatenateAffine(const Matrix4 &m2) const
		{
			assert(isAffine() && m2.isAffine());

			return Matrix4(
					m[0][0] * m2.m[0][0] + m[0][1] * m2.m[1][0] + m[0][2] * m2.m[2][0],
					m[0][0] * m2.m[0][1] + m[0][1] * m2.m[1][1] + m[0][2] * m2.m[2][1],
					m[0][0] * m2.m[0][2] + m[0][1] * m2.m[1][2] + m[0][2] * m2.m[2][2],
					m[0][0] * m2.m[0][3] + m[0][1] * m2.m[1][3] + m[0][2] * m2.m[2][3] + m[0][3],

					m[1][0] * m2.m[0][0] + m[1][1] * m2.m[1][0] + m[1][2] * m2.m[2][0],
					m[1][0] * m2.m[0][1] + m[1][1] * m2.m[1][1] + m[1][2] * m2.m[2][1],
					m[1][0] * m2.m[0][2] + m[1][1] * m2.m[1][2] + m[1][2] * m2.m[2][2],
					m[1][0] * m2.m[0][3] + m[1][1] * m2.m[1][3] + m[1][2] * m2.m[2][3] + m[1][3],

					m[2][0] * m2.m[0][0] + m[2][1] * m2.m[1][0] + m[2][2] * m2.m[2][0],
					m[2][0] * m2.m[0][1] + m[2][1] * m2.m[1][1] + m[2][2] * m2.m[2][1],
					m[2][0] * m2.m[0][2] + m[2][1] * m2.m[1][2] + m[2][2] * m2.m[2][2],
					m[2][0] * m2.m[0][3] + m[2][1] * m2.m[1][3] + m[2][2] * m2.m[2][3] + m[2][3],

					0, 0, 0, 1);
		}

		/** 3-D Vector transformation specially for an affine matrix.
		  @remarks
		  Transforms the given 3-D vector by the matrix, projecting the 
		  result back into <i>w</i> = 1.
		  @note
		  The matrix must be an affine matrix. @see Matrix4::isAffine.
		  */
		inline Vector3f transformAffine(const Vector3f& v) const
		{
			assert(isAffine());

			return Vector3f(
					m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3], 
					m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3],
					m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3]);
		}

		/** 4-D Vector transformation specially for an affine matrix.
		  @note
		  The matrix must be an affine matrix. @see Matrix4::isAffine.
		  */
		inline Vector4f transformAffine(const Vector4f& v) const
		{
			assert(isAffine());

			return Vector4f(
					m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] * v.w, 
					m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] * v.w,
					m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] * v.w,
					v.w);
		}
};

/* Removed from Vector4f and made a non-member here because otherwise
   OgreMatrix4.h and OgreVector4f.h have to try to include and inline each 
   other, which frankly doesn't work ;)
   */
inline Vector4f operator * (const Vector4f& v, const Matrix4& mat)
{
	return Vector4f(
			v.x*mat[0][0] + v.y*mat[1][0] + v.z*mat[2][0] + v.w*mat[3][0],
			v.x*mat[0][1] + v.y*mat[1][1] + v.z*mat[2][1] + v.w*mat[3][1],
			v.x*mat[0][2] + v.y*mat[1][2] + v.z*mat[2][2] + v.w*mat[3][2],
			v.x*mat[0][3] + v.y*mat[1][3] + v.z*mat[2][3] + v.w*mat[3][3]
			);
}
/** @} */
/** @} */

#endif
